The ring oscillator has a delay at each stage (in this case by the R and C at the gate, with an odd number of stages. Thus the digital signal flows from one end of the ring to the other with a speed determined by the delay. When it gets back to the start, the signal is inverted, due to the odd number of stages. and the signal propagates down the ring again with opposite polarity. Thus the signal keeps inverting and propagating around the ring, giving a digital oscillation.